dorsal/arxiv
View SchemaInfinite qubit rings with maximal nearest neighbor entanglement: the Bethe ansatz solution
| Authors | U. V. Poulsen, T. Meyer, D. Bruss, M. Lewenstein |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512214 |
| URL | https://arxiv.org/abs/quant-ph/0512214 |
| DOI | 10.1103/PhysRevA.73.052326 |
| Journal | Phys. Rev. A 73, 052326 (2006) |
Abstract
We search for translationally invariant states of qubits on a ring that maximize the nearest neighbor entanglement. This problem was initially studied by O'Connor and Wootters [Phys. Rev. A {\bf 63}, 052302 (2001)]. We first map the problem to the search for the ground state of a spin 1/2 Heisenberg XXZ model. Using the exact Bethe ansatz solution in the limit of an infinite ring, we prove the correctness of the assumption of O'Connor and Wootters that the state of maximal entanglement does not have any pair of neighboring spins ``down'' (or, alternatively spins ``up''). For sufficiently small fixed magnetization, however, the assumption does not hold: we identify the region of magnetizations for which the states that maximize the nearest neighbor entanglement necessarily contain pairs of neighboring spins ``down''.
{
"annotation_id": "0874c4b8-2ab1-406b-825e-87f0ede47258",
"date_created": "2026-03-02T18:02:23.777000Z",
"date_modified": "2026-03-02T18:02:23.777000Z",
"file_hash": "113278e553aea5b63c9e0a2d33f9e7d0bacaa30105a63e04d0861953437ef4fc",
"private": false,
"record": {
"abstract": "We search for translationally invariant states of qubits on a ring that\nmaximize the nearest neighbor entanglement. This problem was initially studied\nby O\u0027Connor and Wootters [Phys. Rev. A {\\bf 63}, 052302 (2001)]. We first map\nthe problem to the search for the ground state of a spin 1/2 Heisenberg XXZ\nmodel. Using the exact Bethe ansatz solution in the limit of an infinite ring,\nwe prove the correctness of the assumption of O\u0027Connor and Wootters that the\nstate of maximal entanglement does not have any pair of neighboring spins\n``down\u0027\u0027 (or, alternatively spins ``up\u0027\u0027). For sufficiently small fixed\nmagnetization, however, the assumption does not hold: we identify the region of\nmagnetizations for which the states that maximize the nearest neighbor\nentanglement necessarily contain pairs of neighboring spins ``down\u0027\u0027.",
"arxiv_id": "quant-ph/0512214",
"authors": [
"U. V. Poulsen",
"T. Meyer",
"D. Bruss",
"M. Lewenstein"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.052326",
"journal_ref": "Phys. Rev. A 73, 052326 (2006)",
"title": "Infinite qubit rings with maximal nearest neighbor entanglement: the Bethe ansatz solution",
"url": "https://arxiv.org/abs/quant-ph/0512214"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "e86147b2-45bf-483d-9b78-b6d3b45180c3",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}